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### Section 3.4 : The Definition of a Function

3. Determine if the following relation is a function.

$\left\{ {\left( {2,1} \right),\left( {9,10} \right),\left( { - 4,10} \right),\left( { - 8,1} \right)} \right\}$

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Start Solution

Here is the set of 1st components (i.e. the first number in the ordered pair) and the set of the 2nd components (i.e. the second number in the ordered pair.

${1^{st}}{\mbox{ components : }}\left\{ { - 8, - 4,2,9} \right\}\hspace{0.25in}\hspace{0.25in}\hspace{0.25in}{2^{nd}}{\mbox{ components : }}\left\{ {1,10} \right\}$ Show Step 2

Pick any number from the list of 1st components and identify all the ordered pairs with that number as the 1st component and list all the 2nd components from those ordered pairs. In this case no matter which number you pick from the 1st list there is exactly one number in the second list.

Therefore, this relation is a function.

Note that each number in the 2nd list does have two numbers associated with it from the 1st list. That is not an issue however. We only have an issue if numbers from the 1st list have more than one number from the 2nd list associated with it.